On Beamforming with the Single-Sideband Transform

In this paper, we examine the use of the Single-Sideband Transform (SSBT) for convolutive beamformers. We explore its unique properties and implications for beamformer design. Our study sheds light on the tradeoffs involved in using the SSBT in beamforming applications, offering insights into both its strengths and limitations. Despite the advantage of having real-valued coefficients, we show that the convolution handling of the transform presents challenges that impact fundamental beamforming principles. When compared to the Short-Time Fourier Transform (STFT), the SSBT displays lower robustness, especially in scenarios involving mismatch and modeling noise. Notably, we establish a direct equivalence between the SSBT and STFT when using identical transform parameters, enabling their seamless interchangeability and joint use in time-frequency signal enhancements. We validate our theoretical findings through realistic simulations using the Minimum-Power Distortionless Response beamformer. These simulations illustrate that although the STFT performs marginally better than the SSBT under optimal conditions, it outperforms significantly in non-ideal scenarios.